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Cauchy–Pompeiu representations for higher order elliptic equations in the unit ball
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Published/Copyright:
November 22, 2010
Abstract
In this paper we consider the Pompeiu operator in the higher dimensional complex unit ball. The explicit form of its iteration is given. The operator is iterated just once leading to some particular solution to an inhomogeneous bianalytic system. We prove the explicit form of this iteration. Moreover, some further properties, e.g., the kernel space, of the Pompeiu operator are discussed, which gives an application to the pluriharmonic differential system.
Keywords.: Pompeiu formula; higher order complex partial differential equation; pluriharmonic system
Received: 2010-07-27
Revised: 2010-08-11
Published Online: 2010-11-22
Published in Print: 2011-May
© de Gruyter 2011
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Keywords for this article
Pompeiu formula;
higher order complex partial differential equation;
pluriharmonic system
Articles in the same Issue
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- Existence results for a mixed boundary value problem with Sturm–Liouville equation
- On solutions of a nonlinear wave equation derived from brain activity modeling
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